A138292 E.g.f. satisfies A(x) = exp(x*A(x^2)).

1, 1, 1, 7, 25, 121, 841, 9871, 80977, 869905, 10776241, 131366071, 1821918121, 27671299657, 460068491065, 8716820294911, 162728020119841, 3217989767498401, 69343322972016097, 1533322325194196455

Offset: 0

Author

Paul D. Hanna, Mar 13 2008

Keywords

• nonn

Examples

			E.g.f: A(x) = 1 + x + 1/2*x^2 + 7/6*x^3 + 25/24*x^4 + 121/120*x^5 +...
Log(A(x)) = x + x^3 + 1/2*x^5 + 7/6*x^7 + 25/24*x^9 + 121/120*x^11 +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Programs

Maxima

T(n,m):=if n=m then 1 else (1+(-1)^(n-m))/2*((n-m)/2)!*sum(m^k*T((n-m)/2,k)/(k!*((n-m-2*k)/4)!),k,1,(n-m)/2);
makelist(T(2*n-1,1),n,1,20); /* Vladimir Kruchinin, Mar 18 2015 */

PARI

{a(n)=local(A=1); for(i=0,n-1,A=exp(x*subst(A,x,x^2+x*O(x^n))));n!*polcoeff(A,n)}

Formula

a(n) = T(2*n+1), where T(n,m) = (1+(-1)^(n-m))/2*((n-m)/2)!*sum(k=1..(n-m)/2, m^k*T((n-m)/2,k)/(k!*((n-m-2*k)/4)!)), n>m, T(n,n)=1. - Vladimir Kruchinin, Mar 18 2015

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/2)} (2*k+1) * a(k) * a(n-1-2*k) / (k! * (n-1-2*k)!). - Seiichi Manyama, Nov 28 2023